Customers arrive at a movie theater at the advertised movie time only to find th
ID: 3151208 • Letter: C
Question
Customers arrive at a movie theater at the advertised movie time only to find that they have to sit through several previews and prepreview ads before the movie starts. Many complain that the time devoted to previews is too long (The Wall Street Journal, October 12, 2012). A preliminary sample conducted by The Wall Street Journal showed that the standard deviation of the amount of time devoted to previews was four minutes. Use that as a planning value for the standard deviation in answering the following questions.
a. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 75 seconds, what sample size should be used? Assume 95% confidence.
55
22
31
40
b. If we want to estimate the population mean time for previews at movie theaters with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.
62
98
25
40
A.55
B.22
C.31
D.40
Explanation / Answer
A)
Note that
n = z(alpha/2)^2 s^2 / E^2
where
alpha/2 = (1 - confidence level)/2 = 0.025
Using a table/technology,
z(alpha/2) = 1.959963985
Also,
s = sample standard deviation = 4 min = 240 s
E = margin of error = 75
Thus,
n = 39.33653832
Rounding up,
n = 40 [ANSWER, D]
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b)
Note that
n = z(alpha/2)^2 s^2 / E^2
where
alpha/2 = (1 - confidence level)/2 = 0.025
Using a table/technology,
z(alpha/2) = 1.959963985
Also,
s = sample standard deviation = 240
E = margin of error = 1 min = 60 s
Thus,
n = 61.46334113
Rounding up,
n = 62 [ANSWER, A]
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